Integral conditions for Hardy-type operators involving suprema

• Autores: Martin Krepela
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 68, Fasc. 1, 2017, págs. 21-50
• Idioma: inglés
• DOI: 10.1007/s13348-016-0170-6
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• Resumen

  • We characterize the validity of the weighted inequality (∫∞0[sup?∈[?,∞)?(?)∫∞??(?)d?]??(?)d?)1?≤?(∫∞0??(?)?(?)d?)1? for all nonnegative functions g on (0,∞) , with exponents in the range 1≤?<∞ and 0

    Moreover, we give an integral characterization of the inequality (∫∞0[sup?∈[?,∞)?(?)?(?)]??(?)d?)1?≤?(∫∞0??(?)?(?)d?)1? being satisfied for all nonnegative nonincreasing functions f on (0,∞) in the case 0